I doubt it's the well pump, assuming the pressure switch is working properly and the pipes are not frozen. Yes, the pump uses a non-trivial amount of power, but the duty cycle should be low, even with the additional water usage. It should only run on demand (based on the pressure switch by the pressure tank).
Since you have actual readings, what are the actual kWh differences? You should be able to roughly estimate the electric usage of your RV, at least to a rough order of magnitude sort of value, and see if the usage increase seems reasonable. It may partly be a fluke or feature of the billing structure, where the cost goes up significantly over certain usage threshholds. It could also be a plain old billing error.